Let \(\Theta _0=\lbrace \underline{\theta }\in \Theta : \theta _1\le \theta _2\rbrace  \)  be the restricted parameter space. There is an extensive literature on estimation of \(\theta _1\)  and \(\theta _2\)  (simultaneously as well as componentwise) when it is known apriori that \(\underline{\theta }\in \Theta _0\) . Most of the early studies were focussed around finding restricted maximum likelihood estimators (under the restriction that \(\underline{\theta }\in \Theta _0\) ) and studying their properties (see, for example, [1]}, [2]}, [3]}, [4]}, [5]} and [6]}). A natural question that arises in these problems is whether the unrestricted maximum likelihood estimator(s) (MLE) and/or unrestricted best location (scale) equivariant estimator(s) (BLEE (BSEE)) can be improved by exploiting the prior information that \( \underline{\theta }\in \Theta _0 \) . Many researchers have studied this and related aspects of the problem. Some of the contributions are due to [7]}, [8]}, [9]}, [10]}, [11]}, [12]}, [13]}, [14]}, [15]}, [16]}, [17]}, [18]}, [19]}, [20]}, [21]}, [22]}, [23]}, [24]}, [25]}, [26]}, [27]}, [28]}, [29]}, [30]}, [31]}, [32]}, [33]}, [34]} and [35]}. For a few contributions to this problem under general setting (general probability model and/or general loss function) readers may refer to [36]}, [37]}, [20]}, [39]} and [40]}. For a detailed account of contributions in this area of research one may refer to the research monograph by [41]}.
